Wash leeks well and trim the root, and the dark green leaves. If using larger leek, halve them lengthwise and rinse.
In a medium sized skillet with a tight-fitting lid, add the olive oil. Heat over a. medium high flame.
Add the leeks and let sear, about five minutes. Turn and sear on the other side. They should be golden brown. Add wine and use a spatula to scraoe up the browned bits at the bottom of the skillet. Add water or stock, if using, and salt and pepper to taste. Reduce heat to a gentle simmer, cover, and cook until soft, about 10-15 minutes.
While the leeks are cooking, in a small cup, mix cornstarch with a splash of water and stir vigorously with a fork until dissolved and there are no lumps.
Remove lid from leeks. Poke with a fork. They should be soft. Add the cornstarch and swirl pan to blend. Let leeks simmer another two minutes.
Turn off heat and place leeks and sauce on a serving dish. Drizzle balsamic vinegar over the leeks. You ca serve this hot, warm, or at room temperature.
